MKM and the NIST DLMF

1
MKM and the NIST DLMF

• Dan Lozier
• National Institute of Standards and Technology
• Gaithersburg, MD 20899-8910

2
Traditional Methods of KM

• Handbooks, dictionaries, encyclopedias, atlases
• Springer-NY search
• Keyword handbook 1125 hits
• Handbook in title/subtitle 802 hits
• CRC Press search
• Handbook in title/subtitle, mathematics as
  subject/discipline 41 hits

3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
New Methods of KM for Math

• Stimulus
• CD/DVD, web sites, digital technology
• Interactive graphics (scientific visualization)
• Computer algebra, theorem provers
• Key research areas
• Math notation and definition
• Presentation/representation of math
• Math-aware search
• Hardware/software standards
• Formal methods

9
NIST Digital Library of Mathematical Functions
Project

• - project conceived
• 1998 - sample chapter prototype web site
• 1999 - NSF funding received
• 2000 2004
• Math content development, editing, validation
• Web development, inc. search graphics
• 2005 book published, web site released

10
Personnel

• 4 principal editors
• 10 associate editors
• 35 authors
• 25 validators
• 15 NIST staff

11
(No Transcript)
12
(No Transcript)
13
DLMF Web Site

• Features
• Math content
• Metadata
• Interactive graphics
• Math-aware search
• Demonstration

14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
DLMF Equation Search System
DLMF Database
Query Input
Query Processing
Search Engine
Query Output
Presentation Module
25
Query Expression and Entry

• Simplified, Latex-like query language
• Operators symbols that can be expressed with 1
  or 2 keyboard strokes are so entered
• Otherwise, alphabetical names are used (both
  full-names and short-hand names)
• \ not needed
• and () are equivalent

26
Examples
Ops Entry Ops Entry
Arith ops - / Power, super
, ? - , - Subscript _
, lt , gt , ,
? , ? , - ? , not lt ! , !lt
Goes to -gt ?, ? gt , ltgt
? , ? int, sum 8 infinity
? nebla v sqrt
27
Query Results 2 Choices

• Document list
• Links to DLMF sections
• Matching equations highlighted
• Equation list
• Created on-the-fly
• Links to containing document, positioned with
  matching equation at top of window

28
Recent Developments

• Mathematica and Maple nomenclature
• function names
• order of arguments
• Wild cards
• matches any one token
• \ matches any alphanumeric string in a token
• Null in argument list, e.g. Eulers generalized
  beta integral Betaz0,z1,,

29
DLMF Search Demonstrations

• Mathematica and Maple Illustrations
• Equation Search Page

30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
Legendre Functions
39
(No Transcript)
40
(No Transcript)
41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
Spheroidal Wave Functions
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
(No Transcript)
53
SW.6 Functions of Complex Argument
54
Implications for MKM

• For a given family of SF there exist
• many alternative notations
• a wide variety of useful definitions
• Increased complications when numerical
  computation is considered
• We want to be able to move freely among them
• Real variables are hard enough
• Complex variables are much harder

55
Future Directions at NIST

• (Complete development of basic content)
• (Publish book, release initial web site)
• Improve web site
• XML/MathML
• Content MathML
• Improved search (XQUERY)
• Rudimentary, at least, equation equivalences
• Tables graphs on demand
• Possible second edition, possible new subject area